Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×A4×GL(2,ℤ/4) |
| Fitting | C26×C3 ⋊ C3×D3 |
1960 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 1960 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 2 generators on 15 points:
(2,4)(5,8)(6,7)(9,12,10)(13,14,15);(1,2)(3,4)(6,7,8)(11,12)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72215293, D3×A4×GL(2,ℤ/4), #72252927 |
| maximal normal subgroup of | C3×#72215293, D3×A4×GL(2,ℤ/4), #72252927 |
| maximal quotient of | A4×#63694⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,4)(5,8)(6,7)(9,12,10)(13,14,15), (1,2)(3,4)(6,7,8)(11,12));